factor/contrib/math/utils.factor

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Factor
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IN: math-contrib
USING: errors kernel sequences math sequences-internals namespaces arrays ;
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: deg>rad pi * 180 / ; inline
: rad>deg 180 * pi / ; inline
: lcm ( a b -- c )
#! Smallest integer such that c/a and c/b are both integers.
2dup gcd nip >r * r> /i ; foldable
: mod-inv ( x n -- y )
#! Compute the multiplicative inverse of x mod n.
gcd 1 = [ "Non-trivial divisor found" throw ] unless ;
foldable
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: each-bit ( n quot -- )
over zero? pick -1 number= or [
2drop
] [
2dup >r >r >r 1 bitand r> call r> -1 shift r> each-bit
] if ; inline
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: (^mod) ( n z w -- z^w )
1 swap [
1 number= [ dupd * pick mod ] when >r sq over mod r>
] each-bit 2nip ; inline
: ^mod ( z w n -- z^w )
#! Compute z^w mod n.
over 0 < [
[ >r neg r> ^mod ] keep mod-inv
] [
-rot (^mod)
] if ; foldable
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: powers ( n x -- { 1 x x^2 x^3 ... } )
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#! Output sequence has n elements.
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<array> 1 [ * ] accumulate ;
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: ** ( u v -- u*v' ) conjugate * ; inline
: c. ( v v -- x )
#! Complex inner product.
0 [ ** + ] 2reduce ;
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: sum ( v -- n ) 0 [ + ] reduce ;
: product ( v -- n ) 1 [ * ] reduce ;
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: proj ( u v -- w )
#! Orthogonal projection of u onto v.
[ [ v. ] keep norm-sq v/n ] keep n*v ;
: minmax ( seq -- min max )
#! find the min and max of a seq in one pass
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1./0. -1./0. rot [ dup pick max -rot nip pick min -rot nip ] each ;
: absminmax ( seq -- min max )
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#! find the absolute values of the min and max of a seq in one pass
minmax 2dup [ abs ] 2apply > [ swap ] when ;
SYMBOL: almost=-precision .000001 almost=-precision set
: almost= ( a b -- bool )
2dup - abs almost=-precision get < [
2drop t
] [
2array absminmax dup almost=-precision get * >r - abs r>
dup 0 < [ >= ] [ <= ] if
] if ;
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TUPLE: frange from step length ;
C: frange ( from step to -- seq )
#! example: 0 .01 10 <frange> >array
>r pick - swap [ / ceiling 1+ ] keep -rot swapd r>
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[ set-frange-length ] keep
[ set-frange-step ] keep
[ set-frange-from ] keep ;
: decrement-length ( frange -- )
[ frange-length 1- ] keep set-frange-length ;
: <frange-no-endpt> ( from step length -- seq )
<frange> dup decrement-length ;
M: frange length ( frange -- n )
frange-length ;
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: increment-start ( frange -- )
[ [ frange-from ] keep frange-step + ] keep set-frange-from ;
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: frange-range ( frange -- range )
[ frange-step ] keep frange-length 1- * ;
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M: frange nth ( n frange -- obj )
[ frange-step * ] keep frange-from + ;
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: nseq-swap ( a b seq -- seq )
#! swap indices a,b in seq
3dup [ nth ] keep swapd [ nth ] keep
>r >r rot r> r> swapd set-nth -rot set-nth ;
! : pivot ( left right index seq -- )
! [ nth ] keep [ nseq-swap ] 3keep ;
SYMBOL: step-size .01 step-size set ! base on arguments
: (limit) ( count diff quot -- x quot )
pick 10 > [ "Not converging fast enough" throw ] when
[ call ] keep >r 2dup swap - 0 < [ "not converging" throw ] when
2dup almost= rot drop r>
swap [ step-size [ 2 / ] change rot 1+ -rot (limit) ] unless ;
: limit ( quot -- x )
.1 step-size set [ call ] keep step-size [ 2 / ] change 0 -rot (limit) 2drop ;
! take elements n at a time and apply the quotation, forming a new seq
: group-map ( seq n quot -- seq )
pick length pick /
[ [ >r pick pick r> -rot pick over * [ + ] keep swap rot <slice> pick call
, ] repeat ] { } make 2nip nip ;
: nths ( start n seq -- seq )
-rot pick length <frange-no-endpt> [ over nth ] map nip ;
! take a set of every nth element and apply the quotation, forming a new seq
! { 1 2 3 4 5 6 } 3 [ sum ] skip-map -> { 1 4 } { 2 5 } { 3 6 } -> { 5 7 9 }
: skip-map ( seq n quot -- seq )
pick length pick /mod
0 = [ "seq length must be a multiple of n" throw ] unless
1 <= [ "seq must be 2n or longer" throw ] when
over [ [ dup >r >r pick pick r> rot swapd nths over call , r> ] repeat ] { } make 2nip nip ;
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: nth-rand ( seq -- elem ) [ length random-int ] keep nth ;